This pilot clinical trial studies copper Cu 64 (64Cu) tetra-azacyclododecanetetra-acetic acid (DOTA)-trastuzumab positron emission tomography (PET)/computed tomography (CT) in studying patients with gastric, or stomach cancer. Diagnostic procedures, such as copper Cu 64-DOTA-trastuzumab PET/CT, may help doctors study the characteristics of tumors and choose the best treatment.